The Gregorian reform of 1582: epacts, moons and a corrected Easter

In the sixteenth century the error in the calendar was evident to anyone who knew how to watch the sky. The Julian year, with a leap day every four years, was about eleven minutes longer than the solar year, and over more than twelve centuries the spring equinox had slipped from 21 March towards the 11th. The calendar's moons, too, calculated with the nineteen-year cycle, lagged several days behind the real ones. The date of Easter risked losing all connection with the spring full moon.

Lilius, Clavius and the bull Inter gravissimas

The solution adopted by Pope Gregory XIII was based on the project of the Calabrian physician and astronomer Luigi Lilio, known as Aloysius Lilius, who died in 1576 before seeing it applied. The manuscript was presented by his brother Antonio, and the commission charged with the reform, in which the Jesuit mathematician Christopher Clavius played a leading role, examined, developed and defended it. The bull Inter gravissimas was signed on 24 February 1582.

To bring the equinox back to 21 March, ten days were removed: Thursday 4 October 1582 was followed by Friday 15 October. For the future it was established that century years would be leap years only if divisible by four hundred: 1600 and 2000 were, while 1700, 1800 and 1900 were not. With this rule the discrepancy with the Sun is reduced to about one day in three thousand years.

Epacts in place of the golden number

The most ingenious part of the reform concerned the Moon. In place of the golden number, which marked the new moons in the Julian calendar, Lilius proposed epacts: a number from 0 to 29 expressing the age of the Moon at the start of the year. The epacts are corrected periodically by two equations: the solar one, which accounts for the leap days removed, and the lunar one, which compensates for the error accumulated by the nineteen-year cycle.

The lunar correction is applied eight times in two thousand five hundred years, bringing the ecclesiastical moons forward by one day. The system is complex, but it has one merit: it can last for centuries without new reforms. Clavius published the full explanation in 1603, in a substantial work devoted to the Roman calendar restored by Gregory XIII, which remains the standard commentary on the Gregorian calendar.

Catholic, Protestant and Orthodox countries

The reform was adopted at once by Italy, Spain, Portugal and the Polish-Lithuanian Commonwealth, and a few months later by France. Many Protestant countries waited longer: the Protestant German states conformed in 1700, Great Britain and its colonies in 1752, Sweden in 1753. Russia adopted the Gregorian calendar only in 1918, after the revolution, and Greece in 1923.

The Orthodox Churches, by contrast, largely continue to calculate Easter with the Julian calendar and the old lunar cycle. This is why Orthodox Easter sometimes coincides with the Catholic and Protestant one, but more often falls one or more weeks later, up to five. In 2025 the two dates coincided, on 20 April, and the 1700th anniversary of the Council of Nicaea revived the debate on a common date.

The Gregorian reform is often remembered for the ten vanished days, but its heart was Easter, and therefore the Moon. The system of epacts still sets the date of the feast in the Catholic Church and in the Protestant Churches, and its principles are found in the algorithms with which mathematicians and astronomers, beginning with Carl Friedrich Gauss in 1800, have put Easter into a formula.